Fuzzy Congruence Relations and Fuzzy Order Filters

Author

Luo, Minxia ; Cao, Feilong ; Yao, Ning

Author_Institution

Dept. of Inf. & Math. Sci., China Jiliang Univ., Hangzhou, China

Volume

7

fYear

2009

fDate

14-16 Aug. 2009

Firstpage

30

Lastpage

33

Abstract

In this paper, we introduce the notion of fuzzy congruence relation, fuzzy order filter of the adjoint semigroup M(X) of BCK-algebra X. We discuss some characterizations of fuzzy congruence relations and fuzzy order filters. In the adjoint semigroup of a positive implicative BCK-algebra with condition(S), every fuzzy congruence relation may induce a fuzzy order filter of M(X), and every fuzzy order filter may induce a fuzzy congruence relation. Moreover, we show that there is a bijection from the set of all fuzzy congruence relations to the set of all fuzzy order filters of semigroup M(X) which is the adjoint semigroup of a positive implicative BCK-algebra X with condition(S).

Keywords

fuzzy set theory; group theory; BCK-algebra; adjoint semigroup; fuzzy congruence relations; fuzzy order filters; Algebra; Fuzzy sets; Fuzzy systems; Information filtering; Information filters; Mathematics; adjoint semigroup; fuzzy congruence relation; fuzzy order filter;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems and Knowledge Discovery, 2009. FSKD '09. Sixth International Conference on

Conference_Location

Tianjin

Print_ISBN

978-0-7695-3735-1

Type

conf

DOI

10.1109/FSKD.2009.337

Filename

5359942